Chapter 6.4, Problem 80AYU

To determine

To calculate: the average rate of change of $f$ from $0$ to $\frac{\pi }{2}$ .

Answer to Problem 80AYU

Solution: $-\frac{4}{\pi }$

Explanation of Solution

  $\begin{array}{l}f(x)=\cos (2x)\\ x_1=0\\ x_2=\frac{\pi }{2}\end{array}$

Compute rate of change $m,$ using $m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

  $\begin{array}{l}m=\frac{\cos (2.\frac{\pi }{2})-\cos 0}{\frac{\pi }{2}-0}\\ m=\frac{\cos \pi -\cos 0}{\frac{\pi }{2}}\\ m=\frac{-1-1}{\frac{\pi }{2}}\\ m=-\frac{4}{\pi }\end{array}$